B.Ed

If you have any doubt, let me clear it. Anyone can obtain a degree from any university within the country. Similarly, everyone has a right to get a job under any state government. It is our right to freedom. Now, if you have completed B.Ed from Andhra University and want to do a job in Odisha, there will be no obstacle, go ahead.
Good luck.

Both are good options, you can do B.Ed after your graduation but D.El.Ed just after your 10+2. With B.Ed, you can apply for both TGT and PGT. But for PGT you need to complete your Master's degree. D.El.Ed is a Diploma course. So with this, you can apply for the elementary level post that means from nursery to class 8th.

You are eligible to apply for B.Ed.
The eligibility is you need to have with at least 55 % marks either in the Bachelor's degree and/or in the master's degree in Sciences/Social Sciences/Commerce/Humanity, Bachelors in Engineering.

Mostly the colleges offer admission to students who have passed the course from UGC approved college.
AICTE college will grant admission or not is totally at the college discretion.

That really depends on the subject you opt to teach. If you are pursuing M.Ed, you should pursue a subject which you feel comfortable teaching. Since you have already chosen English and Maths as your subjects for B.Ed, you should select a subject in the same domain, so that you have in-depth knowledge of a particular subject and you can then pursue a teaching job in the same subject.

You can pursue B.Ed through distance.

If you opted for any subject as major then the marks of the major subject will only be considered, otherwise, average marks of all the subjects ate considered for pass course.

PGDCA may help you to choose your method papers in B.Ed and you can become a computer teacher later. If you don't do PGDCA, it won't matter.